Simulating Hamiltonian dynamics in a programmable photonic quantum processor using linear combinations of unitary operations

• URL: http://arxiv.org/abs/2211.06723v1
• Date: Sat, 12 Nov 2022 18:49:41 GMT
• Title: Simulating Hamiltonian dynamics in a programmable photonic quantum processor using linear combinations of unitary operations
• Authors: Yue Yu, Yulin Chi, Chonghao Zhai, Jieshan Huang, Qihuang Gong and Jianwei Wang
• Abstract summary: We modify the multi-product Trotterization and combine it with the oblivious amplitude amplification to simultaneously reach a high simulation precision and high success probability. We experimentally implement the modified multi-product algorithm in an integrated-photonics programmable quantum simulator in silicon.
• Score: 4.353492002036882
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Simulating the dynamic evolutions of physical and molecular systems in a quantum computer is of fundamental interest in many applications. Its implementation requires efficient quantum simulation algorithms. The Lie-Trotter-Suzuki approximation algorithm, also well known as the Trotterization, is a basic algorithm in quantum dynamic simulation. A multi-product algorithm that is a linear combination of multiple Trotterizations has been proposed to improve the approximation accuracy. Implementing such multi-product Trotterization in quantum computers however remains experimentally challenging and its success probability is limited. Here, we modify the multi-product Trotterization and combine it with the oblivious amplitude amplification to simultaneously reach a high simulation precision and high success probability. We experimentally implement the modified multi-product algorithm in an integrated-photonics programmable quantum simulator in silicon, which allows the initialization, manipulation and measurement of four-qubit states and a sequence of linearly combined controlled-unitary gates, to emulate the dynamics of a coupled electron and nuclear spins system. Theoretical and experimental results are in good agreement, and they both show the modified multi-product algorithm can simulate Hamiltonian dynamics with a higher precision than conventional Trotterizations and a nearly deterministic success probability. We certificate the multi-product algorithm in a small-scale quantum simulator based on linear combinations of operations, and this work promises the practical implementations of quantum dynamics simulations.

Related papers

• A hybrid quantum-classical algorithm for multichannel quantum scattering of atoms and molecules [62.997667081978825]
  We propose a hybrid quantum-classical algorithm for solving the Schr"odinger equation for atomic and molecular collisions. The algorithm is based on the $S$-matrix version of the Kohn variational principle, which computes the fundamental scattering $S$-matrix. We show how the algorithm could be scaled up to simulate collisions of large polyatomic molecules.
  arXiv  Detail & Related papers  (2023-04-12T18:10:47Z)
• Importance sampling for stochastic quantum simulations [68.8204255655161]
  We introduce the qDrift protocol, which builds random product formulas by sampling from the Hamiltonian according to the coefficients. We show that the simulation cost can be reduced while achieving the same accuracy, by considering the individual simulation cost during the sampling stage. Results are confirmed by numerical simulations performed on a lattice nuclear effective field theory.
  arXiv  Detail & Related papers  (2022-12-12T15:06:32Z)
• Reducing circuit depth in adaptive variational quantum algorithms via effective Hamiltonian theories [8.24048506727803]
  We introduce a new transformation in the form of a product of a linear combination of excitation operators to construct the effective Hamiltonian with finite terms. The effective Hamiltonian defined with this new transformation is incorporated into the adaptive variational quantum algorithms to maintain constant-size quantum circuits.
  arXiv  Detail & Related papers  (2022-01-23T09:38:46Z)
• QuOp_MPI: a framework for parallel simulation of quantum variational algorithms [0.0]
  QuOp_MPI is a Python package designed for parallel simulation of quantum variational algorithms. It presents an object-orientated approach to quantum variational algorithm design.
  arXiv  Detail & Related papers  (2021-10-08T08:26:09Z)
• Quantum algorithms for quantum dynamics: A performance study on the spin-boson model [68.8204255655161]
  Quantum algorithms for quantum dynamics simulations are traditionally based on implementing a Trotter-approximation of the time-evolution operator. variational quantum algorithms have become an indispensable alternative, enabling small-scale simulations on present-day hardware. We show that, despite providing a clear reduction of quantum gate cost, the variational method in its current implementation is unlikely to lead to a quantum advantage.
  arXiv  Detail & Related papers  (2021-08-09T18:00:05Z)
• Quantum-Classical Hybrid Algorithm for the Simulation of All-Electron Correlation [58.720142291102135]
  We present a novel hybrid-classical algorithm that computes a molecule's all-electron energy and properties on the classical computer. We demonstrate the ability of the quantum-classical hybrid algorithms to achieve chemically relevant results and accuracy on currently available quantum computers.
  arXiv  Detail & Related papers  (2021-06-22T18:00:00Z)
• Fixed Depth Hamiltonian Simulation via Cartan Decomposition [59.20417091220753]
  We present a constructive algorithm for generating quantum circuits with time-independent depth. We highlight our algorithm for special classes of models, including Anderson localization in one dimensional transverse field XY model. In addition to providing exact circuits for a broad set of spin and fermionic models, our algorithm provides broad analytic and numerical insight into optimal Hamiltonian simulations.
  arXiv  Detail & Related papers  (2021-04-01T19:06:00Z)
• Quantum Markov Chain Monte Carlo with Digital Dissipative Dynamics on Quantum Computers [52.77024349608834]
  We develop a digital quantum algorithm that simulates interaction with an environment using a small number of ancilla qubits. We evaluate the algorithm by simulating thermal states of the transverse Ising model.
  arXiv  Detail & Related papers  (2021-03-04T18:21:00Z)
• Randomizing multi-product formulas for Hamiltonian simulation [2.2049183478692584]
  We introduce a scheme for quantum simulation that unites the advantages of randomized compiling on the one hand and higher-order multi-product formulas on the other. Our framework reduces the circuit depth by circumventing the need for oblivious amplitude amplification. Our algorithms achieve a simulation error that shrinks exponentially with the circuit depth.
  arXiv  Detail & Related papers  (2021-01-19T19:00:23Z)
• Low-depth Hamiltonian Simulation by Adaptive Product Formula [3.050399782773013]
  Various Hamiltonian simulation algorithms have been proposed to efficiently study the dynamics of quantum systems on a quantum computer. Here, we propose an adaptive approach to construct a low-depth time evolution circuit. Our work sheds light on practical Hamiltonian simulation with noisy-intermediate-scale-quantum devices.
  arXiv  Detail & Related papers  (2020-11-10T18:00:42Z)
• Realistic simulation of quantum computation using unitary and measurement channels [1.406995367117218]
  We introduce a new simulation approach that relies on approximating the density matrix evolution by a sum of unitary and measurement channels. This model shows an improvement of at least one order of magnitude in terms of accuracy compared to the best known approaches.
  arXiv  Detail & Related papers  (2020-05-13T14:29:18Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.